Aviezri Fraenkel's Home Page

This page lists some of my preprints, recent reprints, and indicates how to access my Games Bibliography. Also my special favorite, the Responsa Project, is mentioned briefly.

Some Preprints

A.S. Fraenkel and N.B. Ho, When are translations of P-positions of Wythoff's game P-positions?, Preprint.

G.E. Andrews, A.S. Fraenkel and J.A. Sellers, Characterizing the number of $m$-ary partitions modulo $m$, to appear in Amer. Math. Monthly (about mid-2015).

L. Goldberg and A.S. Fraenkel, Extensions of Wythoff's game, Preprint.

A.S. Fraenkel and U. Larsson, Take-Away Games on Beatty's Theorem and the Notion of Invariance, Preprint.

A.S. Fraenkel, Integrating and Rejuvenating Old and New Gems, To appear in Studies in Honour of Yaacov Choueka.

A.S. Fraenkel and U. Peled, Harnessing the Unwieldy MEX Function, To appear in Games of No Chance 4.

A.S. Fraenkel, The Rat game and the Mouse game, To appear in Games of No Chance 4.

A.S. Fraenkel, Complementary balanced words over an arbitrary finite alphabet.

  • A.S. Fraenkel, Im Hatzibur, l'ma'an hazulat, in Hebrew.

  • A.S. Fraenkel, lzichro shel Tzvi Betzer za"l, in Hebrew.

  • A.S. Fraenkel, Tzadikim Urshaim b'mas' Horayot, in Hebrew. Preprint.

  • A.S. Fraenkel, Leket Al Birkat Hachamah, in Hebrew. Preprint.

  • A.S. Fraenkel, Hachodesh hazeh lachem rosh chodashim, in Hebrew. Preprint.

  • A.S. Fraenkel, Ichud olamot, in Hebrew. Preprint.

  • A.S. Fraenkel, Mah'peichat hamach'sheiv bcheikeir eitz haTorah, in Hebrew. Preprint.

  • A.S. Fraenkel, Tzvi Betzer Z"L -- gareis, dayeik v'yakir, in Hebrew. Preprint.

    Recent Reprints

    A.S. Fraenkel, R.A. Hearn and A.N. Siegel, Theory of combinatorial games, Chapter 15 in: Handbook of Game Theory, Volume 4 (H. Peyton Young and Shmuel Zamir, eds.), pp. 811- 859, Elsevier 2015.

    A. Fink, A.S. Fraenkel and C. Santos, Lim Is not Slim, Internat. J. Game Theory (2014) 43:269-281 DOI 10.1007/s00182-013-0380-z http://link.springer.com/article/10.1007%2Fs00182-013-0380-z#page-1.

    A.S. Fraenkel, Beating Your Fractional Beatty Game Opponent and: What's the Question to Your Answer? , in: Advances in Combinatorics, in Memory of Herbert S. Wilf, Proc. Waterloo Workshop on Computer Algebra, I.S. Kotsireas and E.V. Zima, eds., May 2011, pp. 175-186, Springer 2013.

    A.S. Fraenkel and Y. Tanny, A Class of Wythoff-Like Games , Proc. INTEGERS Conference, Carrollton, Georgia, Oct. 26-29, 2011, in: INTEGERS, Electr. J. Combinat. Number Theory 12(B) (2013) #A7, 18pp. Also in Combinatorial Number Theory, pp. 91-107, de Gruyter 2013. [Archive of INTEGERS.]

    A.S. Fraenkel, Ratwyt, In memory of Martin Gardner, The College Math. J., March 2012, pp. 160-164.

    A.S. Fraenkel, The vile, dopey, evil and odious game players, Discrete Math. 312 (2012) 42-46, special volume in honor of the 80th birthday of Gert Sabidussi.

    A.S. Fraenkel, Aperiodic subtraction games, Electronic J. Combinatorics vol. 18(2) P19 12pp., 2011. http://www.combinatorics.org/Journal/journalhome.html

    S. Blanco and A.S. Fraenkel, Tromping Games: Tiling with Trominoes, Proc. INTEGERS Conference, in honor of the birthdays of Melvyn Nathanson and Carl Pomerance, Carrollton, Georgia, Oct. 14-17, 2009, in: INTEGERS, Electr. J. Combinat. Number Theory 11(A) (2011) #6, 29pp.

    U. Larsson, P. Hegarty and A.S. Fraenkel, Invariant and dual subtraction games resolving the Duchene-Rigo conjecture, Theoretical Computer Science 412 (2011), 729-735.

    A.S. Fraenkel, From enmity to amity. Amer. Math. Monthly 117 (2010), 646--648.

    A.S. Fraenkel, Complementary Iterated Floor Words and the Flora Game. SIAM J. on Discrete Math 24 (2010), 570--588.

    E. Duchene, A.S. Fraenkel, R.J. Nowakowski and M. Rigo, Extensions and restrictions of Wythoff's game preserving its P-positions. J. Combinat. Theory A 117 (2010), 545--567.

    J. Bell, E. Charlier, A.S. Fraenkel, M. Rigo, A decision problem for ultimately periodic sets in non-standard numeration systems. Internat. J. Algebra Computat 19 (2009), 6, 809--839.

    A.S. Fraenkel and E. Reisner, The game of End-Wythoff, in Games of No Chance 3, Proc. BIRS Workshop on Combinatorial Games, July 2005, Banff, Alberta, Canada, MSRI Publ. (M.H. Albert and R.J. Nowakowski, eds.), Vol. 56, Cambridge University Press, Cambridge, pp. 329-347, 2009.

    A.S. Fraenkel, The cyclic Butler University game, in: Mathematical Wizardry for a Gardner (E. Pegg Jr, A.H. Schoen, and T. Rodgers, eds.), in honor of Martin Gardner, pp. 97-105, A K Peters, Natick, MA, 2009.

    E. Duchene, A.S. Fraenkel, S. Gravier and R.J. Nowakowski, Another bridge between Nim and Wythoff, Australasian J. of Combinatorics 44 (2009), 43--56.

    S. Artstein-Avidan, A.S. Fraenkel and V. Sos, A two-parameter family of an extension of Beatty sequences, Discrete Math 308 (2008) 4578-4588.

    A.S. Fraenkel, Games played by Boole and Galois, Discrete Appl. Math., 156 (2008) 420-427.

    P.J. Davis and A.S. Fraenkel, Remembering Philip Rabinowitz, Notices AMS 54 (2007) 1502-1506. Reprinted, with the permission of the AMS, in The Birth of Numerical Analysis (A. Bultheel, R. Cools, eds.) World Scientific (2009) 179-185.

    A.S. Fraenkel, The Raleigh game. in: Combinatorial Number Theory, Proc. INTEGERS Conference 2005, in celebration of the 70th birthday of Ronald Graham, Carrollton, Georgia, Oct. 27-30, 2005; B. Landman, M. Nathanson, J. Nesetril, R. Nowakowski, C. Pomerance, eds., de Gruyter, pp. 199-208, 2007. Also appeared in INTEGERS, Electr. J. Combinat. Number Theory 7(2) (2007) #13, 11pp., special volume in honor of Ron Graham.

    A.S. Fraenkel and A. Kontorovich, The Sierpinski sieve of Nim-varieties and binomial coefficients. in: Combinatorial Number Theory, Proc. Integers Conference 2005, in celebration of the 70th birthday of Ronald Graham, Carrollton, Georgia, Oct. 27-30, 2005; B. Landman, M. Nathanson, J. Nesetril, R. Nowakowski, C. Pomerance, eds., de Gruyter, pp. 209-227, 2007. Also appeared in INTEGERS, Electr. J. Combinat. Number Theory 7(2) (2007) #14, 19pp., special volume in honor of Ron Graham.

    A.S. Fraenkel, Why are games exciting and stimulating?, Math Horizons February 2007, 5--7; 32--33. A German translation, by Niek Neuwahl, was poster-displayed at the ``Games & Science, Science & Games" exhibition, which took place in Goettingen, July 17 -- Aug 21, 2005. It was selected as runner up for an EMS Article Competition 2005 for the educated layman.

    A.S. Fraenkel, Nim is easy, chess is hard --- but why??, J. Internat. Computer Games Assoc. 29 (2006) 203--2006. Earlier shorter version appeared in Plus Mag. (electronic) issue 40, pluschat section, Sept., 2006.

    A.S. Fraenkel, Euclid and Wythoff games, Discrete Math. 304 (2005) 65--68.

    Aviezri S. Fraenkel and Jamie Simpson, An extension of the periodicity lemma to longer periods, Discrete Appl. Math. 146 (2005) 146-155 (special issue of 12th Annual Symposium on Combinatorial Pattern Matching). Preliminary version appeared in Proc. 12th Annual Sympos. Combinatorial Pattern Matching, Jerusalem, Israel, July 1--4, 2001 (A. Amir and G. M. Landau, eds.), Lecture Notes in Computer Science, Springer, Berlin, pp. 98--105) (invited).

    A.S. Fraenkel, New games related to old and new sequences. INTEGERS, Electronic J. Combinat. Number Theory 4 (2004) #G06, 18pp. http://www.integers-ejcnt.org . First version appeared in Advances in Computer Games, Proc. 10-th Advances in Computer Games Conference (ACG-10), Nov. 2003, Graz, Austria (H.J. van den Herik, H. Iida, E.A. Heinz, eds.), pp. 367--382, Kluwer.

    A.S. Fraenkel, Complexity, appeal and challenges of combinatorial games, Expanded version of a keynote address at Dagstuhl Seminar Feb.~17--22, 2002, Theoretical Computer Science 313 (2004) 393-415, special issue on Algorithmic Combinatorial Game Theory.

    S.P. Fekete, R. Fleischer, A.S. Fraenkel and M. Schmitt, Traveling salesmen in the presence of competition, Theoretical Computer Science 313 (2004) 377-392, special issue on Algorithmic Combinatorial Game Theory.

    E.D. Demaine, R. Fleischer, A.S. Fraenkel and R.J. Nowakowski, Open problems at the 2002 Dagstuhl Seminar on Algorithmic combinatorial game theory, Theoretical Computer Science 313 (2004) 539-543, special issue on Algorithmic Combinatorial Game Theory (Appendix B).

    A.S. Fraenkel and Dalia Krieger, The structure of complementary sets of integers: a 3-shift theorem, Internat. J. Pure and Appl. Math. 10 (2004) 1--49.

    Aviezri S. Fraenkel and Ofer Rahat, Complexity of error-correcting codes derived from combinatorial games, Proc. Intern. Conference on Computers and Games CG'2002, Edmonton, Alberta, Canada, July 2002 (Y. Bj\"{o}rnsson, M.\ M\"{u}ller, J. Schaeffer, eds.), Lecture Notes in Computer Science LNCS 2883, pp. 201--212, Springer 2003.

    Aviezri S. Fraenkel, Jamie Simpson and Mike Paterson, On abelian circular squares in binary words. In: Paul Erdos and his Mathematics II, Bolyai Soc., Mathematical Studies 11, Budapest 2002, pp. 329--338. An earlier version entitled ``On weak circular squares in binary words'' appeared in Proc. 8th Annual Symposium on Combinatorial Pattern Matching, Aarhus, Denmark, June 30--July 2, 1997 (A. Apostolico and J. Hein, eds.), Lecture Notes in Computer Science, Springer, Berlin, pp. 76--82).

    A.S. Fraenkel, Two-player games on cellular automata, in More Games of No Chance, Proc. MSRI Workshop on Combinatorial Games, July 10--28, 2000, Berkeley, CA (R. J. Nowakowski, ed.), Cambridge University Press, Cambridge, Vol. 42, 2002, pp. 279--306.

    A.S. Fraenkel, Arrays, numeration systems and Frankenstein games, Theoretical Computer Science 282 (2002) 271--284 (special "FUN in Algorithms" issue).

    A.S. Fraenkel, Mathematical Chats Between Two Physicists, in Puzzlers' Tribute: A Feast for the Mind, honoring Martin Gardner (D. Wolfe and T. Rodgers, eds.), A K Peters, 2002, pp. 315--325.

    A.S. Fraenkel, Virus versus mankind, in: Proc. 2nd Intern. Conference on Computer Games CG'2000, Hamamatsu, Japan, Oct. 2000, Lecture Notes in Computer Science, Springer (T. Marsland, I. Frank, eds.), 2001, pp. 204--213.

    A.S. Fraenkel, T. Seeman and J. Simpson The subword complexity of a two-parameter family of sequences, Electronic J. Combinatorics vol. 8(2) R10, 2001 http://www.combinatorics.org/Journal/journalhome.html

    A.S. Fraenkel, A Selection Of Mathematical Board Games, Abstract Presented at Board Games in Academia III, Florence, April 12--15, 1999. Proceedings Board Games in Academia III, pp. 46--67.

    A.S. Fraenkel and D. Zusman, A New Heap Game, Theoretical Computer Science 252 (2001) 5--12 (special "Computers and Games issue"). Initial version appeared in Lecture Notes in Computer Science 1558, Proc. 1-st Intern. Conference on Computer Games, Tsukuba, Japan, Nov. 1998, pp. 205--211, 1999.

    A.S. Fraenkel and O. Rahat, Infinite cyclic impartial games, Theoretical Computer Science 252 (2001) 13-22 (special "Computers and Games issue"). Initial version appeared in Lecture Notes in Computer Science 1558, Proc. 1-st Intern. Conference on Computer Games, Tsukuba, Japan, Nov. 1998, pp. 212--221, 1999.

    A.S. Fraenkel, Recent results and questions in combinatorial game complexities, Expanded version of invited lecture at Ninth Australasian Workshop on Combinatorial Algorithms, Perth, Western Australia, 27---30 July 1998, Theoret. Comput. Sci. 249 (2000) 265--288. Conference version in: Proc. AWOCA98 --- Ninth Australasian Workshop on Combinatorial Algorithms, (C.S. Iliopoulos, ed.), pp. 124--146.

    A.S. Fraenkel, On the recurrence f(m+1)=b(m)f(m)-f(m-1) and applications, Discrete Mathematics 224 (2000) 273--279 (Note).

    A.S. Fraenkel and S.T. Klein, Information retrieval from annotated texts, J. Amer. Soc. for Information Sciences 50 (1999) 845--854.

    A.S. Fraenkel and Jamie Simpson, The exact number of squares in Fibonacci words, Theoret. Comput. Sci. 218 (1999) 95--106 (special Words issue).

    A.S. Fraenkel, Protein folding, spin glass and computational complexity, Expanded form of invited paper presented at DNA Based Computers III, Proc. DIMACS Workshop (H. Rubin and D. H. Wood, Eds.), June 23--25, 1997, University of Pennsylvania, DIMACS Series in Discrete Mathematics and Theoretical Computer Science Vol. 48, AMS, 1999, pp. 101--121.

    A.S. Fraenkel, Heap games, numeration systems and sequences, Annals of Combinatorics 2 (1998) 197--210.

    U.Blass, A.S. Fraenkel and R. Guelman, How far can Nim in disguise be stretched?, J. Combin. Theory (Ser. A) 84 (1998) 145--156.

    A.S. Fraenkel, The Responsa storage and retrieval system---whither? The Hebrew version: Proyect hashut: avar, hoveh---v'gam atid? appeared in Dinei Yisrael 19 (1997-98) 253--270.

    A.S. Fraenkel and Michal Ozery, Adjoining to Wythoff's game its P-positions as moves, Theoretical Computer Science 205 (1998) 283--296.

    A.S. Fraenkel, Multivision: a game of arbitrarily long play, Amer. Math. Monthly 105 (1998) 923--928.

    A.S. Fraenkel and Jamie Simpson, How many squares can a string contain? J. Combin. Theory Ser. A 82 (1998) 112--120. Errata: In Table 1, the number of maximal words (last column) should be 6 and 72 for n=3 and n=12 respectively. These corrections do not otherwise affect the results of the paper. We thank Troy Vasiga for pointing out the first of these typos.

    A.S. Fraenkel, Combinatorial game theory foundations applied to digraph kernels , Electronic J. of Combinatorics 4(2) (1997) R10, 17pp. (Wilf Festschrift).

  • A.S. Fraenkel, Al hilchot hashacheyn hachiloni (in Hebrew). Hatzofe Erev shabbat Mas'ey, ha-tashsach, Aug. 1, 2008, p. 40.

  • A.S. Fraenkel, Sifrei Chayim v'sifrei Meitim P'tuchim lfanav (in Hebrew). Hama'ayan 48, Issue 1, Tishrei ha-tashsach, September 2007, pp. 34--37,

  • A.S. Fraenkel, Hirhurim m'atim al proyekt hashu''t (in Hebrew) {\it Hatzofe\/} Erev Shabbat Hagadol, 11 Nissan ha-tashsaz, March 30, 2007, pp. 11,14.

  • A.S. Fraenkel, Madua ein korin korban musaf shel shabbat b'shabbat -- B, in Hebrew. Hama'ayan 47, Issue 3, Nissan Ha-Tashsaz, March 2007, pp. 25--29.

  • A.S. Fraenkel, Al t'filot ha'amida shel arvit, shacharit, mincha umisfei rosh chodesh, in Hebrew. Moriya 27, Issue 9-10, pp. 85--89, Tevet Ha-tashsav, Jan 2006.

  • A.S. Fraenkel, Korban pesach b'veit hamikdash: She'elat z'man umakom, in Hebrew. Sefer hazikaron ``Yoseif Da'at" l'zichro shel Yoseif Aharon Nitzan za"l (Memorial volume commemorating the memory of the late Yosef Aharon Nitzan), Sh'vat Ha-tashsav (Feb 2006), pp. 238--244.

  • A.S. Fraenkel, Vaykonein Yirm'yahu al Yoshiyahu, in Hebrew. Hatzofe Erev Shabbat Pinchas, ha-tashsad, July 9, 2004, p. 14.

  • A.S. Fraenkel, Mikra'ot b'chag hashavu'ot v'darchei heyseik (in Hebrew). Dedicated to the memory of Prof. Shalom (Freddy) Hirshfeld, za''l, Hatzofe Erev Chag Hashavuot, ha-tashsad, May 25, 2004, p. 13.

  • A.S. Fraenkel, Meshech Chochma l'sar haTorah, in Hebrew. Dedicated to the memory of Dr. Zvi Betzer, za"l, Hatzofe Erev Shabbat Ki Tavo, ha-tashsag, Sept 12, 2003, p. 12, 14

  • A.S. Fraenkel, Sukkot B'Shavu'ot, in Hebrew. Hatzofe Erev Shabbat Sh'lach-L'cha, ha-tashsag, June 20, 2003, p. 14

  • A.S. Fraenkel, hitmachut, mumchiyut utchumim, in Hebrew. Hatzofe Erev Shabbat Vayeishev, erev chag haChanukah, ha-tashsag, Nov 29, 2002, p. 11.

  • S. Yedid and A.S. Fraenkel, Hashofeit kol ha'aretz lo ya'aseh mishpat?, in Hebrew. Dedicated to the memory of Dr. Zvi Betzer, za"l, Hatzofe Erev Shabbat Vayeira, ha-tashsag, Oct 25, 2002, p. 14.

  • A.S. Fraenkel, R'galim, korbanot, avodah zarah, in Hebrew. Hatzofe Erev chag haSukkot, ha-tashsag, Sept 20, 2002, p. 13.

  • A.S. Fraenkel, Bein yachid l'tzibbur biymei din, in Hebrew. Hatzofe 1st part: Erev Rosh Hashanah, ha-tashsag, Sept 6, 2002, pp. 12--13; 2nd part: Erev Yom Kippur, Sept 15, 2002, p. 4.

  • A.S. Fraenkel, He'arot z'irot (2), in Hebrew. Hatzofe (under the title "Zeicheir liy'tzi'at mitzrayim") Erev Shabbat Hagadol, 13 Nissan, ha-tashsa; April 4, 2001, pp. 12-13.

  • A.S. Fraenkel He'arot z'irot (1), in Hebrew. Hatzofe Erev Shabbat Mishpatim, parashat Sh'kalim, 1 Adar, ha-tashsa; Feb 23, 2001, pp. 14-15.

  • A.S. Fraenkel M'sirut nefesh ugvurat nefesh, in Hebrew. Hatzofe Erev Shabbat Bo, 9 Sh'vat, ha-tashsa; Feb 2, 2001, p. 10.

  • A.S. Fraenkel Al ``Meshech Chochma'', in Hebrew. Hatzofe (under the title 'Bein n'vuat emet linvuat sheker (al echad meiekronot haparshanut shel ha"meshech chochmah")', Erev Shabbat Tol'dot, 4 Kisleiv ha-tashsa; Dec 1, 2000, p. 8.

  • A.S. Fraenkel, Bein yehudim lishe'einam yehudim, in Hebrew. Hatzofe, Appeared in two parts: Erev Shavuot, 5 Sivan ha-tashas, June 8, 2000; and Erev Shabbat B'ha'alotcha, 13 Sivan ha-tashas; June 16, 2000.

  • A.S. Fraenkel, Simaniyot baMikra, in Hebrew. Hatzofe, Erev Shabbat K'doshim, 30 Nissan ha-tashas; May 5, 2000.

  • A.S. Fraenkel, Hadramah hashnatit, in Hebrew. Hatzofe, Erev Shabbat Vayigash, 8 Teiveit ha-tashas; Dec. 17, 1999, p. 12.

  • A.S. Fraenkel, T'filah: keifel teivot umiktzat hanhagot shel shatz, in Hebrew. Hatzofe, Erev Rosh Hashanah ha-tashas, 29 Elul ha-tashnat; Sept. 10, 1999, pp. 16--17.

  • A.S. Fraenkel, Chidon otzrot yisraeil, in Hebrew. In Memorial Volume commemorating Rabbi Aaron Nathan Weiss zatzal. A preliminary version appeared in Hatzofe, Erev Shabbat Bamidbar, Yom Shichrur Yerushalayim, 28 Iyar ha-tashnat; May 14, 1999. p. 14.

  • A.S. Fraenkel, Kabalat ol malchut shamayim, in Hebrew. Morashteinu vol. 13, 33-38, Sept. 1999. Preliminaty version appeared in Hatzofe, Erev Shabbat Vay'chi, 13 Teiveit ha-tashnat; January 1, 1999, p. 12.

  • A.S. Fraenkel, K'az kein atah, in Hebrew. Hatzofe, Erev Pesach, 14 Nissan ha-tashnat; March 31, 1999, p. 14.

  • A.S. Fraenkel, Bameh maftirin uvameh ein maftirin, in Hebrew. Hatzofe, Erev Shabbat Nitzavim-Vayeilech, 24 Elul ha-tashnaz; September 26, 1997, pp. 7--8.

  • A.S. Fraenkel, Madua ein korin korban musaf shel shabbat b'shabbat, in Hebrew. Hatzofe, Erev Shabbat Pin'chas, 20 Tamuz ha-tashnaz; July 25, 1997, p. 6.

  • A.S. Fraenkel, Hafradat rashuyot tifkudit bein kohen gadol, melech v'sarim?, in Hebrew. Hatzofe, Erev Shabbat Acharei Mot, 25 Nissan ha-tashnaz; May 2, 1997, p. 7.

  • A.S. Fraenkel, Haramba"m, haRashb"a uMaran al ta'ut b'seifer Torah, in Hebrew. Moriya 21 Issue 5--6, Adar Beit ha-tashnaz; 1997, pp. 109--110.

  • A.S. Fraenkel, L'olam heveih adam koneis divrei Torah k'lalim, in Hebrew. Hatzofe, Erev Shabbat Ki Tissa, 21 Adar Aleph ha-tashnaz; Feb. 28, 1997, p. 8.

  • A.S. Fraenkel, Nusach birkat "me'ein shalosh" utfilato shel kohen gadol b'yom hakipurim, in Hebrew. Sh'ma'atin 125, Chanukah ha-tashnav; 1995, pp. 80-87.

    Games Bibliography

    A dynamic bibliography on Combinatorial Games, currently containing over 1700 items is a Dynamic Survey (D2, originally 1994) in the Dynamic Surveys section of the Electronic Journal of Combinatorics. For the latest update, view/download one of the files: gb.dvi, gb.pdf. Corrections, suggestions and comments are welcome. They should be sent to me by email.

    Electronic Journals

    Some of the leading refereed electronic journals in mathematics can be accessed from here, via the courtesy of the AMS. We mention especially the influential Electr. J. Combinatorics, and the younger, yet prestigeous, INTEGERS -- Electronic Journal of Combinatorial Number Theory. It has a combinatorial games section.

    The Responsa Storage and Retrieval Project

    The Responsa Project stores the largest compilation of Jewish databases (it should actually be considerably larger). The most sophisticated search tools for Hebrew and Aramaic text processing (which should be much more sophisticated!) have been developed for searching it. Its philosophy, described from two viewpoints, can be found at: Yaacov Choueka, Aviezri Fraenkel's Work in Information Retrieval and Related Areas, A.S. Fraenkel, The Responsa storage and retrieval system---whither? The Hebrew version: Proyect hashut: avar, hoveh---v'gam atid? appeared in Dinei Yisrael 19 (1997-98) 253--270.

    The Good Countries and the Good People Therein

  • Australia: Rony Attar, Jamie Simpson

  • Belgium; Emilie Charlier, Michel Rigo

  • Canada: Jason Bell, British Columbia; James Jones, Alberta; the late Anton Kotzig, Quebec; Richard Nowakowski, Nova Scotia; Gert Sabidussi, Quebec

  • China: Rudolf Fleischer

  • Czech Republic: Martin Loebl, Jaroslav Nesetril

  • France; Eric Duchene, Sylvain Gravier

  • Germany: Sandor Fekete, Matthias Schmitt

  • Hungary: the late Paul Erdos, Vera Sos

  • Israel: Zvia Agur, Shiri Artstein-Avidan, Alexander Barabash, Marc Berger, Uri Blass, Viktor Bronstein, Yaacov Choueka, Meir Cohen, Nachum Dershowitz, Joseph Dueck, N. Duvdevani, the late Joseph Gillis, Lior Goldberg, Elisheva Goldschmidt, Romina Guelman, Ron Holzman, Tomi Klein, Dalia Krieger, the late Dan Loewenthal, Mordechai Lorberbom, the late Moshe Mor, Mordechai Mushkin, Michal Ozery, Udi Peled, Ofer Rahat, Benny Reuter, D. Schindler, Tamar Seeman, E. Segal, the late Michael Shimshoni, Mark Slae, E. Spitz, Yuval Tanny, Uzi Tassa, Barak Weiss, Sinai Yedid (Responsa), Dmitri Zusman

  • Italy: Alberto Apostolico

  • Portugal: Carlos Santos

  • Sweden: Peter Hegarty, Urban Larsson

  • UK: Jonathan Levitt, Mike Paterson

  • USA: George Andrews, PA, Saul Blanco, Itshak Borosh, TX; Michael Boshernitzan, TX; the late David Cantor, CA; Philip J. Davis, RI; Erik Demaine, MA; Roger Eggleton, IL; the late Gerald Estrin, CA; Alexander Felzenbaum, NY; Alex Fink, NC; Michael Garey, NJ; the late Basil Gordon, CA; the late Peter Hammer, NJ; the late Frank Harary, NM; Robert Hearn, CA, Hans Herda, MA; Alan Jaffrey, IL; David Johnson, NJ; Joseph Kahane, NY; Clark Kimberling, IN; Alex Kontorovich, NY; David Lichtenstein, MA; Yehoshua Perl, NJ; Horacio Porta, IL; D. Raab, NY; Edward Reingold, IL; Elnatan Reisner, MD; Prashant Saxena, IL;Thomas Schaefer, CA; Edward Scheinerman, MD; James Sellers, PA, Aaron Siegel, CA, Shai Simonson, MA; Kenneth Stolarsky, IL; the late Ernst Straus, CA; the late Rein Turn, CA; Daniel Ullman, DC; Yaacov Yesha, MD

    Vanity of vanities -- all is vanity (Eccl. 1,2)

    1972, Feder Foundation Prize for initiating and creating the Responsa Project.

    1998, Quality Initiative Citation to the Responsa Project for creative, high-quality and visionary projects to celebrate the 50th anniversary of the establishment of the State of Israel.

    2001, The Fraenkel Festschrift volume, Electr, J. of Combinatorics, vol. 8(2).

    2005, Runner up in European Mathematical Society Article Competition.

    2005, Euler Medal recipient of the Institute for Combinatorics and Its Applications. Excerpts from the citation in Bull. ICA 47, May 2006; front of medal, back; photographed by Eli Shechtman.

    2006, Recipient of WEIZAC Medal, at December 5 special seminar, celebrating recognition by the IEEE of the WEIZAC project as a Milestone in the History of Computers. (WEIZAC, constructed at the Weizmann Institute of Science in 1954, was the first electronic digital computer in the Middle East, and one of the first in the world.)

    2007, Elected Meritocrat of Rehovot (Yakir Ha'ir). One of the photos of the ceremony, March 6, 2007. (without recipient and spouse)

    2007, Israel Prize to the Responsa Project, which I initiated and nurtured for decades, beginning in Jan. 1963.

    Wikipedia pages: Hebrew ; English ; German .

    Personal Data

    URL for this homepage is: http://www.wisdom.weizmann.ac.il/~fraenkel

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